Many studies have examined how humans and other animals reestablish a sense of direction following disorientation in enclosed environments. Results showing that geometric shape of an enclosure is typically encoded, sometimes to the exclusion of featural cues, have led to suggestions that geometry might be encoded in a dedicated geometric module. Recently, Miller and Shettleworth (2007) proposed that the reorientation task be viewed as an operant task and they presented an associative operant model that appears to account for many empirical findings from reorientation studies. In this paper we show that, although Miller and Shettleworth's insights into the operant nature of the reorientation task may be sound, their mathematical model has a serious flaw. We present simulations to illustrate the implications of the flaw. We also propose that the output of a simple neural network, the perceptron, can be used to conduct operant learning within the reorientation task and can solve the problem in Miller and Shettleworth's model.

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Human participants were trained to navigate to two geometrically equivalent corners of a parallelogramshaped virtual environment. The unique shape of the environment combined three distinct types of geometric information that could be used in combination or in isolation to orient and locate the goals: the angular amplitudes of the corners, the relative wall length relationships, and the principal axis of symmetry. In testing, participants were placed in manipulated versions of the training environment that tested which types of geometry they had encoded and how angular information weighed in against the other two geometric properties. The test environments were (a) a rectangular environment that removed the angular information, (b) a rhombic environment that removed wall length information and drastically reduced the principal axis, and (c) a reverse-parallelogram-shaped environment that placed angular information against both wall length and principal axis information. Participants chose accurately in the rectangular and rhombus environments, despite the removal of one of the cues. In the conflict test, participants preferred corners with the correct angular amplitudes over corners that were correct according to both wall length relationships and the principal axis. These results are comparable to recent findings with pigeons and suggest that angles are a salient orientation cue for humans.

Abstract-The matching law (Herrnstein 1961) states that response rates become proportional to reinforcement rates; this is related to the empirical phenomenon called probability matching (Vulkan 2000). Here, we show that a simple artificial neural network generates responses consistent with probability matching. This behavior was then used to create an operant procedure for network learning. We use the multiarmed bandit (Gittins 1989), a classic problem of choice behavior, to illustrate that operant training balances exploiting the bandit arm expected to pay off most frequently with exploring other arms. Perceptrons provide a medium for relating results from neural networks, genetic algorithms, animal learning, contingency theory, reinforcement learning, and theories of choice.Index Terms-Instrumental learning, multiarmed bandit, operant conditioning, perceptron, probability matching.

A recent associative model (Miller, N.Y., & Shettleworth, S.J., 2007. Learning about environmental geometry: An associative model. Journal of Experimental Psychology: Animal Behavior Processes B, 33, 191-212) is an influential mathematical account of how agents behave when reorienting to previously learned locations in spatial arenas. However, it is mathematically and empirically flawed. The current article explores these flaws, including its inability to properly predict geometric superconditioning. We trace the flaws to the model's mathematical structure and how it handles inhibition. We then propose an operant artificial neural network model that solves these problems with inhibition and can correctly model both reorientation and superconditioning.